Particle pixels problem
I think the problem you're having is what's sometimes called "fireflies." These are not in the texture, these are part of the render. The short answer is "render more samples." "Progressive" can be useful for this. Just let it render the whole image for as long as you can stand. It'll get a little better with each pass, and you can cancel whenever you want and still have a full image. 

This is usually just a consequence of the probabilistic nature of the Cycles renderer. I'm going to mark this question as a duplicate, but I want to at least point you in the right direction.

One strategy that's not well documented is to render the same image more than one time, but with a different "seed" value for each image (set in the render settings). Stack these results in an image editor (careful with opacity math) to average them together, and the fireflies will be much less apparent.

Check out this other answer about why fireflies happen.

Also look at this question about how to reduce noise.

And lastly, this question about why Cycles has to cast multiple rays per pixel.

Hope that helps!